%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET633+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:08:11 PM UTC 2026
% Result : Theorem 0.26s 1.61s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_15)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th115,conjecture,
! [X1,X2,X3] :
( ( subset(difference(X1,X2),X3)
& subset(difference(X2,X1),X3) )
=> subset(symmetric_difference(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th115) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(commutativity_of_symmetric_difference,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(union_subset,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(union(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_subset) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(i_0_9,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(difference(X1,X2),X3)
& subset(difference(X2,X1),X3) )
=> subset(symmetric_difference(X1,X2),X3) ),
inference(assume_negation,[status(cth)],[prove_th115]) ).
fof(i_0_10,negated_conjecture,
( subset(difference(esk3_0,esk4_0),esk5_0)
& subset(difference(esk4_0,esk3_0),esk5_0)
& ~ subset(symmetric_difference(esk3_0,esk4_0),esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])])]) ).
fof(i_0_11,plain,
! [X26,X27] : symmetric_difference(X26,X27) = union(difference(X26,X27),difference(X27,X26)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
fof(i_0_12,plain,
! [X42,X43] : symmetric_difference(X42,X43) = symmetric_difference(X43,X42),
inference(variable_rename,[status(thm)],[commutativity_of_symmetric_difference]) ).
fof(i_0_13,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
cnf(i_0_14,negated_conjecture,
~ subset(symmetric_difference(esk3_0,esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[i_0_10]) ).
cnf(i_0_15,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_11]) ).
cnf(i_0_16,plain,
symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_12]) ).
fof(i_0_17,plain,
! [X44,X45,X46,X47,X48,X49] :
( ( ~ member(X46,X44)
| member(X46,X45)
| X44 != X45 )
& ( ~ member(X47,X45)
| member(X47,X44)
| X44 != X45 )
& ( ~ member(esk2_2(X48,X49),X48)
| ~ member(esk2_2(X48,X49),X49)
| X48 = X49 )
& ( member(esk2_2(X48,X49),X48)
| member(esk2_2(X48,X49),X49)
| X48 = X49 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_member_defn])])])])])]) ).
fof(i_0_18,plain,
! [X31,X32,X33] :
( ( member(X33,X31)
| ~ member(X33,difference(X31,X32)) )
& ( ~ member(X33,X32)
| ~ member(X33,difference(X31,X32)) )
& ( ~ member(X33,X31)
| member(X33,X32)
| member(X33,difference(X31,X32)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])])]) ).
fof(i_0_19,plain,
! [X28,X29,X30] :
( ~ subset(X28,X29)
| ~ subset(X30,X29)
| subset(union(X28,X30),X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_subset])]) ).
fof(i_0_20,plain,
! [X34,X35,X36,X37,X38] :
( ( ~ subset(X34,X35)
| ~ member(X36,X34)
| member(X36,X35) )
& ( member(esk1_2(X37,X38),X37)
| subset(X37,X38) )
& ( ~ member(esk1_2(X37,X38),X38)
| subset(X37,X38) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_defn])])])])])]) ).
fof(i_0_21,plain,
! [X40,X41] : union(X40,X41) = union(X41,X40),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(i_0_22,plain,
! [X51] : subset(X51,X51),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
cnf(i_0_23,negated_conjecture,
~ subset(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),esk5_0),
inference(rw,[status(thm)],[i_0_14,c_0_15]),
[final] ).
cnf(i_0_24,plain,
union(difference(X1,X2),difference(X2,X1)) = union(difference(X2,X1),difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_16,c_0_15]),c_0_15]),
[final] ).
cnf(i_0_25,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_26,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_27,plain,
( subset(union(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_28,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_29,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_30,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_31,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_32,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_33,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_34,negated_conjecture,
subset(difference(esk4_0,esk3_0),esk5_0),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_35,negated_conjecture,
subset(difference(esk3_0,esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_36,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_37,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_38,axiom,
X1 = X1 ).
cnf(i_0_39,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_40,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_41,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_42,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_38_001,axiom,
X1 = X1 ).
cnf(i_0_39_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_40_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_41_004,axiom,
( X1 != X2
| union(X1,X3) = union(X2,X3) ) ).
cnf(i_0_42_005,axiom,
( X1 != X2
| union(X3,X1) = union(X3,X2) ) ).
cnf(i_0_43_006,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_44_007,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_45_008,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_46_009,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_47,plain,
$false,
inference(scs_inference,[],[i_0_23,i_0_35,i_0_34,i_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET633+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n016.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:31:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.26/1.61 % Version : CSE_E---1.7
% 0.26/1.61 % Problem : theBenchmark.p
% 0.26/1.61 % SZS status Theorem for theBenchmark.p
% 0.26/1.61 % SZS output start CNFRefutation
% See solution above
% 0.26/1.62 % Total time : 1.271s
%------------------------------------------------------------------------------